Geodesic
Numerical solution of a~fluid filtration problem in a~fractured medium by using the domain decomposition method
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 15-27.

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Under consideration are the numerical methods for simulation of a fluid flow in fractured porous media. The fractures are taken into account explicitly by using a discrete fracture model. The formulated single-phase filtering problem is approximated by an implicit finite element method on unstructured grids that resolve fractures at the grid level. The systems of linear algebraic equations (SLAE) are solved by the iterative methods of domain decomposition in the Krylov subspaces using the KRYLOV library of parallel algorithms. The results of solving some model problem are presented. A study is conducted of the efficiency of the computational implementation for various values of contrast coefficients which significantly affect the condition number and the number of iterations required for convergence of the method.
Keywords: filtering, fracturedmedium, discrete fracture model, approximation, flow rate, finite element method, unstructured grid, iterative method. 
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     author = {V. I. Vasil'ev and M. V. Vasil'eva and V. S. Gladkikh and V. P. Ilin and D. Ya. Nikiforov and D. V. Perevozkin and G. A. Prokop'ev},
     title = {Numerical solution of a~fluid filtration problem in a~fractured medium by using the domain decomposition method},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {15--27},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a1/}
}
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V. I. Vasil'ev; M. V. Vasil'eva; V. S. Gladkikh; V. P. Ilin; D. Ya. Nikiforov; D. V. Perevozkin; G. A. Prokop'ev. Numerical solution of a~fluid filtration problem in a~fractured medium by using the domain decomposition method. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 15-27. http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a1/

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